Chicago White Sox's Conor Gillaspie throws to first base on a ground out by Boston Red Sox's Will Middlebrooks in the fifth inning of a baseball game in Boston, Saturday, Aug. 31, 2013. (AP Photo/Michael Dwyer)

Boston Red Sox's Xander Bogaerts, right, reacts after getting the forced out on Chicago White Sox's Josh Phegley (36) but failing to turn the double play on Alejandro De Aza in the third inning of a baseball game in Boston, Saturday, Aug. 31, 2013. (AP Photo/Michael Dwyer)

Acquired in a three-team, seven-player deal July 30 that sent infielder Jose Iglesias to Detroit, Peavy spent four seasons with the White Sox. The 32-year old right-hander went 36-29 after being picked up in a trade from San Diego on July 31, 2009.

"I certainly knew that team in and out," he said. "I did know pretty much for the most part what they were going to do. I think that worked pretty much to my advantage."

Peavy (11-5) allowed two runs and five singles in his sixth start for the Red Sox. He struck out four and walked one while throwing 109 pitches.

Even White Sox manager Robin Ventura could see him working his hitters a certain way.

"He's good at seeing some weaknesses at people and he tried to exploit them," he said. "Today you could see him do it. You could see what he was trying to do. I don't know if it's that easy at the plate, but, from afar, when you're sitting back, you could see him do it."

Ellsbury also scored twice and drove in a run for the AL East-leaders. David Ortiz, who snapped an 0-for-23 stretch with a two-run single in Friday's win, went 2 for 4 with a walk and an RBI in Boston's 15-hit attack.

It was the 11th straight game Boston's pitchers have held an opponent to three or fewer runs, matching the best since April of 1988. According to Elias Sports Bureau, it's the most since 12 in a row in 1915.

"I'm certainly happy I wasn't the one to end it," Peavy said, smiling.

Chicago, last in the AL Central, had won 10 of 12 before dropping the first two of a three-game series against Boston.

Boston broke open a tie game with three runs in the fourth against John Danks (4-11), and then scored again in the fifth.

That was more than enough for Peavy.

"I don't think Jake can be any more amped up than he is in any game," Danks said. "He looked like typical Jake. He had a pretty good game plan and stuck to it. That's why he's had the success he's had over how many years he's played. He's certainly one of the best that's played."

Ellsbury's tiebreaking ground-rule double gave the Red Sox a 3-2 lead. Dustin Pedroia then drove in run with a groundout before Ortiz lined an RBI single to left.

Rookie Xander Bogaerts, regarded as one of the top prospects in baseball, added an RBI single in the fifth that made it 6-2.

Danks gave up six runs, five earned, and 11 hits over five innings. He had won his previous two starts, allowing only two runs in 14 innings.

"I knew I had to be good and simply wasn't," he said. "Jake did what he has to do with a lead."

The Red Sox had grabbed a 1-0 lead in the first on Mike Napoli's RBI single. Chicago tied it on Alejandro De Aza's run-scoring groundout.

Jonny Gomes doubled home a run in the third, but the White Sox tied it again on Avisail Garcia's RBI single.

NOTES: The Red Sox announced a minor trade with Philadelphia during the game, acquiring utility INF John McDonald and cash for Single-A RHP Nefi Ogando. The 38-year old McDonald, a 15-year veteran, played for Pittsburgh, Cleveland, and the Phillies this season, hitting .098 in 45 games. ... Boston manager John Farrell said the club expects to call up three or four players when the rosters expand Sunday. ... White Sox 3B Conor Gillaspie made a diving catch of David Ross' liner. ... Hall of Famer and former Red Sox and White Sox catcher Carlton Fisk was at the game. ... Felix Doubront (10-6, 3.74 ERA) faces Chicago's Andre Rienzo (1-0, 4.21 ERA) in the series finale Sunday. ... Chicago's Adam Dunn is 5 for his last 46. ... Boston finished August 16-12 and Chicago went 16-13.